I understand how you feel but I don't think it's doable. There's an intuitive sense of who is a dealer. And yet all collectors can sell art.
I think part of why you posted is because a lot of the art for sale is "new" inventory. Or "priced to sell" in some cases. I could see it being more fair to bargain on inventory that's been sitting around for years. But offering new inventory and willing to bargain with a smaller audience before it gets shown to the rest of the world might seem less fair to buyers. But can also lead to the dealer selling for less than their "list" price. In theory, the buyers and sellers are still benefiting from the show.
Dealers can always decline offers. They're there to deal. On Dueling Dealers, not every piece sells. But I think it's very rare that someone makes an offer at less than "list" price and the show ends with the piece going unsold.
A better solution would be to expand the universe of viewers (and hopefully buyers). I watch Dueling Dealers on a pretty regular basis (and Dealmakers sometimes). But I've never tried to claim anything. I think it's been mentioned here that it seems like the same few people claim art. Even during the shows, sometimes a piece pops up and there's the expectation that a certain buyer is lurking and should claim the piece, kind of funny. I think last night's show had a lot of pieces sell to more people, so that's good. Maybe it's related to that show having a max price of $2,000.